In order to overcome this difficulty, Harten et al. [1]}, [2]}, [3]}
succeeded by relaxing the TVD condition and allowing the spurious
oscillations to occur in the numerical scheme, but the \(O(1)\)  Gibbs-like
phenomena are essentially prevented. This is the first successful
higher order spatial discretization method for the hyperbolic conservation
laws that achieves the essentially non-oscillatory (ENO) property
and known as ENO schemes. In [1]}, finite-volume ENO method
was studied and shown that, to have a uniform high-order accuracy
right up to the location of any discontinuity. Later, the finite-difference
ENO scheme was developed by Shu and Osher in [5]}, [6]}.
